Monte Carlo methods in finance | Financial models

Brownian model of financial markets

The Brownian motion models for financial markets are based on the work of Robert C. Merton and Paul A. Samuelson, as extensions to the one-period market models of Harold Markowitz and William F. Sharpe, and are concerned with defining the concepts of financial assets and markets, portfolios, gains and wealth in terms of continuous-time stochastic processes. Under this model, these assets have continuous prices evolving continuously in time and are driven by Brownian motion processes. This model requires an assumption of perfectly divisible assets and a frictionless market (i.e. that no transaction costs occur either for buying or selling). Another assumption is that asset prices have no jumps, that is there are no surprises in the market. This last assumption is removed in jump diffusion models. (Wikipedia).

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11. Stocks

Financial Markets (ECON 252) The stock market is the information center for the corporate sector. It represents individuals' ownership in publicly-held corporations. Although corporations have a variety of stakeholders, the shareholders of a for-profit corporation are central since the

From playlist Financial Markets (2008) with Robert Shiller

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2. Utilities, Endowments, and Equilibrium

Financial Theory (ECON 251) This lecture explains what an economic model is, and why it allows for counterfactual reasoning and often yields paradoxical conclusions. Typically, equilibrium is defined as the solution to a system of simultaneous equations. The most important economic mode

From playlist Financial Theory with John Geanakoplos

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16. The Evolution and Perfection of Monetary Policy

Financial Markets (ECON 252) Central Banks, originally created as bankers' banks, implement monetary policy using their leverage over the supply of money and credit standards. Since the Bank of England was founded in 1694, through the gold standard which lasted until the 1930s, and into

From playlist Financial Markets (2008) with Robert Shiller

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10. Debt Markets: Term Structure

Financial Markets (ECON 252) The markets for debt, both public and private far exceed the entire stock market in value and importance. The U.S. Treasury issues debt of various maturities through auctions, which are open only to authorized buyers. Corporations issue debt with investment

From playlist Financial Markets (2008) with Robert Shiller

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13. Banking: Successes and Failures

Financial Markets (ECON 252) Banks, which were first created in primitive form by goldsmiths hundreds of years ago, have evolved into central economic institutions that manage the allocation of resources, channel information about productive activities, and offer the public convenient i

From playlist Financial Markets (2008) with Robert Shiller

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Stock Market Predictions : Python for Finance 10

In previous videos we made a wonderful investment portfolio and now we will use regression analysis to make stock market predictions about the future performance of our portfolio. I’ll be using the ARIMA model for making stock market predictions in this video. It focuses on trying to fit

From playlist Python for Finance

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Pricing Options using Black Scholes Merton

These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. https://amzn.to/2WIoAL0 Check out our website http://www.onfinance.org/ Follow Patrick on twitter here: https://twitter.com/PatrickEBoyle The Black–Scholes or Black–Scho

From playlist Class 3: Pricing Financial Options

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7. Behavioral Finance: The Role of Psychology

Financial Markets (ECON 252) Behavioral Finance is a relatively recent revolution in finance that applies insights from all of the social sciences to finance. New decision-making models incorporate psychology and sociology, among other disciplines, to explain economic and financial phen

From playlist Financial Markets (2008) with Robert Shiller

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Fin Math L5-2: A simple exchange rate model

In this second part of Lesson 5, we consider a simple exchange rate model, which allows us to see the Cameron-Martin theorem in action. The model also introduces a particular version of the exponential martingale that will be essential for us later. I ask you to spend some time reasoning a

From playlist Financial Mathematics

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FinMath L3-1: The Ito-Doeblin formula and the basics of math finance

Welcome to Lesson 3 of Financial Mathematics (Part 1). In this lesson we conclude our introductory discussion on the Ito integral, by addressing the (heuristics of the) Ito-Doeblin formula. Such a result will be very useful for us in the rest of the course. We then introduce important conc

From playlist Financial Mathematics

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23. Options Markets

Financial Markets (ECON 252) Options introduce an essential nonlineary into portfolio management. They are contracts between buyers and writers, who agree on exercise prices and dates at which the buyer can buy or sell the underlying (such as a stock). Options are priced based on the pr

From playlist Financial Markets (2008) with Robert Shiller

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Fin Math L8-1: The EU Call in the Bachelier Model

Welcome to Financial Mathematics. In the 8th lesson we consider different topics. In this first video we look at the value of a EU call, when we change the underlying stochastic process. In particular, we will consider the case of the Bachelier model, in which the Geometric Brownian motio

From playlist Financial Mathematics

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Fin Math L4-2: The two fundamental theorems of asset pricing and the exponential martingale

Welcome to the second part of Lesson 4 of Financial Mathematics. In this video we discuss the two fundamental theorems of asset pricing and we introduce the exponential martingale, an essential tool that we will use as the Radon-Nikodym derivative to move from P to Q in the Cameron-Martin

From playlist Financial Mathematics

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Financial Options Pricing History. How do Investors Price Options?

Financial Options Pricing History. Today we will learn How do Investors Price Options? These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. https://amzn.to/2WIoAL0 Check out our website http://www.onfinance.org/ Follow Patri

From playlist Class 2: An Introduction to Options

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Fin Math L6-2: Pricing a EU call and Historical Volatility.

Welcome to the second part of Lesson 6 of Financial Mathematics. $How can we price a European call, now that we known the Black-Scholes-Merton theorem? What can we say about σ, i.e. volatility? Topics: 00:00 Pricing a EU call 12:28 Volatility in the BSM framework 15:06 Historical volatil

From playlist Financial Mathematics

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Fin Math L5-1: The Cameron-Martin theorem

Welcome to the first part of Lesson 5 of Financial Mathematics. The topic of this video is the important Cameron-Martin theorem, which represents a special case of Girsanov's one. The theorem tell us how to connect a standard Brownian motion and a Brownian motion with drift. Topics: 00:0

From playlist Financial Mathematics

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Options (Lecture 2) by Shashi Jain

Program Summer Research Program on Dynamics of Complex Systems ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE : 15 May 2019 to 12 July 2019 VENUE : Madhava hall for Summer School & Ramanujan hall f

From playlist Summer Research Program On Dynamics Of Complex Systems 2019

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Financial Option Theory with Mathematica -- Basics of SDEs and Option Pricing

This is my first session of my Financial Option Theory with Mathematica track. I provide an introduction to financial options, develop the relevant SDEs (stochastic differential equations), and then apply them to stock price processes and the pricing of (European) options. You can downloa

From playlist Financial Options Theory with Mathematica

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3. Computing Equilibrium

Financial Theory (ECON 251) Our understanding of the economy will be more tangible and vivid if we can in principle explain all the economic decisions of every agent in the economy. This lecture demonstrates, with two examples, how the theory lets us calculate equilibrium prices and all

From playlist Financial Theory with John Geanakoplos

Related pages

Black–Scholes model | Lebesgue measure | Bounded variation | Monte Carlo method | Augmented filtration | Almost surely | Risk | Stochastic differential equation | Stochastic process | Probability space | Continuous function | Lebesgue's decomposition theorem | Self-financing portfolio | Jump diffusion | Brownian motion | Martingale (probability theory) | Frictionless market | Volatility (finance) | Natural filtration | Mathematical finance | Semimartingale | Absolute continuity | Martingale pricing